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Some variants of Lagrange’s mean value theorem
Selecciones Matemáticas, 2020 In this note we prove some variants of Lagrange’s mean value theorem. The main tools to prove these results are some elementary auxiliary functions.
German Lozada-Cruz
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A Mean Value Theorem for Tangentially Convex Functions
Set-Valued and Variational Analysis, 2023 The main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions.
Juan Enrique Martínez-Legaz
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The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel
Advances in Difference Equations, 2018 We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.
Arran Fernandez, Dumitru Baleanu
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Geophysical Research Letters, 2018 Downward continuation can enhance small‐scale sources and improve resolution. Nevertheless, the common methods have disadvantages in obtaining optimal results because of divergence and instability.
Chong Zhang +3 more
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Some new integral inequalities via variant of Pompeii's mean value theorem [PDF]
Mathematica Moravica, 2015 The main of this paper is to establish an inequality providing some better bounds for integral mean by using a mean value theorem. Our results generalize the results of Ahmad et. al in [8].
Sarikaya Zeki Mehmet
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A discrete mean-value theorem for the higher derivatives of the Riemann zeta function [PDF]
Journal of Number Theory, 2021 We show that the $n$th derivative of the Riemann zeta function, when summed over the non-trivial zeros of zeta, is real and positive/negative in the mean for $n$ odd/even, respectively. We show this by giving a full asymptotic expansion of these sums.
C. Hughes, Andrew Pearce-Crump
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Mean Value Theorem and Its Uses
Highlights in Science Engineering and Technology, 2023 The foundation of all mathematical analysis is calculus. The mean value theorem of differential equations and the mean value theorem of integral equations are crucial concepts in calculus. They establish the framework for the entire calculus.
Ying Zhou
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Diameter‐free estimates for the quadratic Vinogradov mean value theorem [PDF]
Proceedings of the London Mathematical Society, 2020 Let s⩾3$s \geqslant 3$ be a natural number, let ψ(x)$\psi (x)$ be a polynomial with real coefficients and degree d⩾2$d \geqslant 2$ , and let A$A$ be some large, non‐empty, finite subset of real numbers. We use Es,2(A)$E_{s,2}(A)$ to denote the number of
Akshat Mudgal
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Nested efficient congruencing and relatives of Vinogradov's mean value theorem [PDF]
Proceedings of the London Mathematical Society, 2017 We apply a nested variant of multigrade efficient congruencing to estimate mean values related to that of Vinogradov. We show that when φj∈Z[t] (1⩽j⩽k) is a system of polynomials with non‐vanishing Wronskian, and s⩽k(k+1)/2 , then for all complex ...
T. Wooley
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Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three [PDF]
, 2015 We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three.
J. Bourgain, C. Demeter, L. Guth
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